Technical Lean evidence record
Checked Artifact: Krein–Milman Theorem (mathlib)
Proof Atlas collected build, no-sorry, axiom, and clean-source evidence directly from the pinned upstream declaration.
ProofAtlas record
What has been checked
These states distinguish upstream identity, local reproduction, review, and Atlas acceptance. This page is part of the public, read-only Mathlib landmark collection.
Mechanical evidence
- Declaration checked
closure_convexHull_extremePoints- Module
Mathlib.Analysis.Convex.KreinMilman- Source file checked
Mathlib/Analysis/Convex/KreinMilman.lean- Package commit
5e932f97dd25535344f80f9dd8da3aab83df0fe6- Build
- passed · transcript retained
- Unfinished proof steps
- None found by the recorded no-sorry scan
- Axiom closure
- Classical.choice, Quot.sound, propext
- Clean collection provenance
- Recorded
Evidence boundary
This page indexes Mathlib's Krein–Milman theorem in a real Hausdorff locally convex topological vector space: every compact convex set s equals closure (convexHull ℝ (s.extremePoints ℝ)). No finite-dimensional hypothesis is present, and the closure is part of the formal conclusion. The set may be empty. The selected declaration does not supply a finite convex representation, a bound on the number of extreme points, or the finite-dimensional strengthening in which closure can sometimes be removed.
This checker record is evidence for the exact formal statement only. It does not establish novelty, transfer a historical acceptance decision, or authorize publication.